prove that triangle ABC is an isosceles,if altitude AD bisects angle BAC
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In ABD and ACD,
∠BAD =∠CAD (since, AD bisects ∠A )
AD = AD (common side)
∠ABD = ∠ACD (since, AD bisects ∠A and it should bisect BD if ABC is a isosceles triangle)
By ASA congruence rule, ABD = ACD.
AB = AC (cpct)
hence, ΔABC is an Isosceles Triangle .
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